Title :
A simplified approach to recovery conditions for low rank matrices
Author :
Oymak, Samet ; Mohan, Karthik ; Fazel, Maryam ; Hassibi, Babak
Author_Institution :
California Inst. of Technol., Pasadena, CA, USA
fDate :
July 31 2011-Aug. 5 2011
Abstract :
Recovering sparse vectors and low-rank matrices from noisy linear measurements has been the focus of much recent research. Various reconstruction algorithms have been studied, including ℓ1 and nuclear norm minimization as well as ℓp minimization with p <; 1. These algorithms are known to succeed if certain conditions on the measurement map are satisfied. Proofs for the recovery of matrices have so far been much more involved than in the vector case. In this paper, we show how several classes of recovery conditions can be extended from vectors to matrices in a simple and transparent way, leading to the best known restricted isometry and nullspace conditions for matrix recovery. Our results rely on the ability to “vectorize” matrices through the use of a key singular value inequality.
Keywords :
information theory; sparse matrices; low rank matrix; matrix recovery; noisy linear measurement; nullspace condition; recovery condition; restricted isometry; singular value inequality; sparse vector; Linear matrix inequalities; Matrix decomposition; Minimization; Noise measurement; Robustness; Sparse matrices; Vectors; rank minimization; sparse recovery;
Conference_Titel :
Information Theory Proceedings (ISIT), 2011 IEEE International Symposium on
Conference_Location :
St. Petersburg
Print_ISBN :
978-1-4577-0596-0
Electronic_ISBN :
2157-8095
DOI :
10.1109/ISIT.2011.6033976